Subgroups of Z12

In[1]:=

z12 = Range[12] - 1

Out[1]=

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

In[2]:=

mod12[x_] := Mod[x, 12]

cyclicGroupGeneratedBy[n_] := Map[mod12, n z12]//Union

cyclicGroupGeneratedBy[4]

Out[4]=

{0, 4, 8}

In[5]:=

subgroupsOfZ12 = Map[cyclicGroupGeneratedBy, z12]//Union//TableForm

Out[5]//TableForm=

0
0 6
0 4 8
0 3 6 9
0 2 4 6 8 10
0 1 2 3 4 5 6 7 8 9 10 11

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